Relics are collectibles Hat Kid can find as she travels the planet. All Relics are pieces of a puzzle, and when put together they will open a pink Time Rift. In order to get all 40 Time Pieces, all relics must be found and completed.
Each Relic is a part of a puzzle, and must be put together in the correct way. To start, you will need to find one of the four podiums around the ship (five with the DLC), then pay pons. Their locations are;
Main Hall, next to the Orb Machine. 50 pons to restore.
Main Hall, next to the slide. 100 pons to restore.
Art Gallery. 150 pons to restore.
Science Lab, which can be entered with the Dweller's Mask after unlocking Alpine Skyline. 200 pons to restore.
With the Seal the Deal DLC a new podium can be found in the Laundry Room. It costs 300 pons to restore.
Nyakuza Metro also adds a new podium in the storage room below the science lab. It costs 250 pons to restore.
In total there 12 Relics (16 with DLC) to find, with two of the puzzles requiring two pieces to solve and three needing four to solve. There are total of 5 complete relics to be made. The pieces listed can be placed in any order after the first one.
Earthling Sitting Device
Research concludes that this thing is very soft to sit on. So soft, that the only logical conclusion is that these is that these are the chairs of this planet. It is not a snack. I tried. It tastes like fabric.
Tiny Train (And Birds?)
Battle of the Birds
This looks like a tiny version of the "Train" the "Birds" use to "Get to work". Are there tiny birds in there? Do they make tiny "Movies"? I don't have time to deal with tiny bird society!
Mockery Of Off-Planet Life
Tin-foil Hat Cow
What the heck! Spaceships don't look like that! Where's the wood? Why is it sucking up cows? This is insulting! I'm gonna sue!
Tri-color Graffiti Kit
These were made for vandalism. Definitely. Even I feel compelled to take these and draw on everything. I can only conclude that this vandalism toolkit must be illegal. That makes this relic extra rare. If only the package hadn't been opened. Only a monster would open the package of a rare item.
' (Seal the Deal DLC)
A fancy metal platform for displaying cakes.
What kind of person would just show them off, though? They're for eating!
...I can't reach the ones on the top shelf.
' (Nyakuza Metro DLC)
Relics can be found in chests and gift boxes around the world. There are several of these, but only 12 Relics. After each Relic is collected, all remaining gift boxes and chest will give out Rift Tokens instead.
Here is a list of all Relic locations
Talk to Cooking Cat when he's on Hat Kid's Spaceship after getting 5 Time Pieces.
Under the aquaduct near the red vault is a treasure chest containing a Relic.
Behind the blue vault is a destructable crate. It hides a tunnel which leads to a cave with a Relic inside.
To the right of the market and in front of the ruined tower, there is a chest near two crows with a Relic.
Next to Seaside Spaghetti at the port.
On the docks near the bazaar is a treasure chest. Inside is the Relic.
Above the boats using the hookshot.
On the beach, jump on the red umbrella by the doors. It will take you up to a platform where you can enter the smaller slide, and has a treasure chest containing a Relic.
In the casino, behind the bar, use the ice hat to pound down into a secret room with a relic in the small room to the back.
Dead Bird Studio
At the crossroad where DJ Grooves is filming, take the right path and traverse the tightrope to a platform with three moon penguins. Avoid them and reach the top to find another tightrope. Cross it to find a chest with a Relic in it.
Dead Bird Studio
After the tepees and before the UFO, before you climb up the plank, turn around and jump onto the building deco, walk toward the very end, then jump toward the platform behind the tepee. Open the chest for a relic.
Murder on the Owl Express
In the VIP room, there is a room labeled "Raven Suite" blocked by crates. Use the brewer hat to destroy them and enter the room. The relic is in a box on top of the bed.
First make sure to get the key in the room with tons of awards. It's in the locked room just before the boss battle, which you get to by dropping down a vent you can't get back up from.
The Snatcher's House
On top of Snatcher's house, which is the big tree right near the start of Act 1. It's a long climb, so be ready for it. Recommended badges are Hover (incase you fall) and Item Magnet (so you collect pons without being distracted by them).
On top of a tall tree stump by the cemetery inside Subcon Village. You can either use the hookshot badge to reach it or a tricky jump.
Inside a tree by the red fire spirits. The entrance is blocked by ice, so use a berry to destroy it.
When entering the swamp from Subcon Village there is a villager who talks about spiders. Homing attack the nearby spiders to land on some ruins. Climb up them to get to a tree house with a relic on its patio.
Alternatively, this area can be reached by going left when on the platform with the bell in front of the wall of ice.
As soon as you enter the Subcon Well, there is a pink mushroom to your left. Jump on it and it will bounce you up to the relic (watch out for the spider!).
Subcon Burning Forest
In the burning forest, there is a phantom bell covered in ice. Use a berry to destroy it so you can climb up the phantom branches nearby. Jump on the mushroom on the fourth branch to be launched up to another branch. The relic is in a tree house in front of the branches.
There is a relic on top of the frozen time ruins, which you can reach by taking the path from the Snatcher's house to the ruins. Start climbing from the opposite side and around to it in order to reach it.
In the ruins near the living room is a large crate in a stone building. Destroy it with the Brewing Hat to reveal a lantern. Hookshot it to swing up to a nearby relic on top of another structure.
Queen Vanessa's Manor
On the roof of Queen Vanessa's Manor. Before entering, find a way up to the roof and keep climbing until you find it.
Queen Vanessa's Manor
In the attic on top of the chandelier. You can use the dweller mask inside the manor without repercussions, so use it to jump across the boxes.
After leaving the first birdhouse you enter on the left side from where you exited, there will be a series of phantom platforms. Use the Dweller's Mask to platform over to the Relic. There's a phantom wall in the way, so you will need to turn off the mask at the right time or you'll fall.
Before entering the second bird house after using the hookshot, you will see a hay bale next to the entrance. Wall run up to the roof (watch out for the punk bird) and use the Brewing Hat to destroy a crate blocking the entrance to this birdhouse. Go down the path it leads you until you enter the first birdhouse again, but this time you'll be on a higher level. Jump over to the other side and you'll find another Relic.
Mystifying Time Mesa (Lava Cake Path)
The area reward for clearing Mystifying Time Mesa. You can reach this after solving the green button puzzle.
After reaching the first checkpoint in the Windmill, drop down and you will find a pon cluster with a Relic inside it. When touched, it will become the last piece in the cluster trail. You don't need to complete the cluster; just get the Relic at the end of it.
This one can be tricky to get, since you're on a time limit from the cluster, and you will need the Dweller's Mask to make to platforms solid. After that, it's probably best to switch to the Time Stop Hat to give you more time to collect the Relic.
If you fail this challenge the first time, it's recommended that you finish the Windmill stage before retrying it, since the cluster won't respawn until you re-enter Alpine Skyline and getting the Time Piece will allow you to warp back to the Windmill, saving you a lot of backtracking time.